基于拓扑结构不变性的3D并行细化算法及其应用

目的双距离场算法提取的骨架居中性不佳,并且算法复杂度高,实时性差。本文提出一种基于拓扑结构不变性的3D细化算法以提取肺气管的骨架。方法首先介绍了基于双距离场和拓扑结构不变性两种算法的基本原理,然后通过对欧拉特性不变性的证明,利用欧拉特性表查询来计算欧拉值,并计算26临域的连通度。利用欧拉特性值和连通度来保证拓扑结构,定义了一种拓扑结构不变的简单点,用并行的细化策略,快速获取单像素宽、连通的骨架中心线。结果将此算法应用于肺气管快速提取骨架中心线,利用已经分割出的高精度肺部气道树来提取骨架中心线。结论基于拓扑结构不变性的3D并行细化算法与基于距离场的骨架提取算法相比得到更光滑、居中性更好的骨架,并且鲁棒性好,对噪声不敏感。

3D parallel thinning algorithm based on topological invariance and its applications

Objective The skeleton is not good at the neutral and not the simplest by the algorithm using the double distance field. An efficient 3-D thinning algorithm was proposed based on topological invariance to extract the skeleton of the pulmonary trachea in this paper. Methods Firstly this paper introduces the two algorithms basic on double distance field and topological invariance. Then through the proof of Euler characteristic invariant,the algorithm calculates the Euler value by using the Euler look-up table( LUT)and computes the connectivity of 26-connected neighbors. The algorithm uses the Euler value and connectivity to ensure topological invariance. Through the definition of simple point with the constant geometric properties and parallel refinement strategy,the algorithm quickly accesses to a single pixel wide and connected skeleton center-line. Results This algorithm can be applied to the pulmonary trachea quickly to extract the skeleton. Conclusions This algorithm achieves better results compared to the skeleton extraction algorithm based on distance field:the skeleton is located near the airway center-line and is connected,smooth,and single pixel wide. The algorithm is robust and not sensitive to noise.